The correct answer is option 4, Tungabhadra. The city of Vijayanagar is located on the banks of this river. The other options are incorrect. Option 1, Kaveri, is a river in southern India, but it does not flow near the city of Vijayanagar. Option 2, Krishna, is another river in southern India, but it also does not flow near Vijayanagar. Option 3, Wainganga, is a river in central India and is not connected to the city of Vijayanagar. Therefore, option 4, Tungabhadra, is the only accurate answer. It is important to carefully read and understand each option before selecting the correct answer.